Problem: Solve for $x$ : $7\sqrt{x} + 10 = 9\sqrt{x} + 9$
Solution: Subtract $7\sqrt{x}$ from both sides: $(7\sqrt{x} + 10) - 7\sqrt{x} = (9\sqrt{x} + 9) - 7\sqrt{x}$ $10 = 2\sqrt{x} + 9$ Subtract $9$ from both sides: $10 - 9 = (2\sqrt{x} + 9) - 9$ $1 = 2\sqrt{x}$ Divide both sides by $2$ $\frac{1}{2} = \frac{2\sqrt{x}}{2}$ Simplify. $\dfrac{1}{2} = \sqrt{x}$ Square both sides. $\dfrac{1}{2} \cdot \dfrac{1}{2} = \sqrt{x} \cdot \sqrt{x}$ $x = \dfrac{1}{4}$